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題組內容

第三部分：計算題

(2) Find at the point (-1,0) if 6x⁴+ 3x²y - 20xy² - 3y³ = 6.

其他申論題

(h) If converges, then converges.

(i) If converges, then converges.

(j) If f : [a,b] → is not continuous, then f(x)dx does not exist.

(3) Find the gradient vector of the function f(x,y) := . Then find the equation of the tangent plane at (2,0).

1. Find the average value of g(x) = |x| - 1 on [-1,3]. Answer:__________

2. Find(x) dx. Answer :_______

3. Evaluatedxdy. Answer :___________

4. Find the values of a and b that makes the function differentiable at x = 0. Answer : _____________

5. Find the tangent line to the curve x2 cos2y - sin y = 0 at (0,π). Answer :__________

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